报告人：胡耀忠(加拿大Alberta大学数学与统计科学系)

报告题目：Transition densities of some singular diffusions

报告摘要：We study the transition probability densities for some singular diffusions, whose drift or diffusion coefficients do not satisfy the global Lipschitz conditions. First we give condition on the coefficients so that the solution remains positive if the initial value is positive. We obtain the asymptotic behaviour of the transition probability density p(t, x, y)=P(x(t)\in dy|x(0)=x) as $y\rightarrow \infty$. Since the solution is positive the support of the transition density  is contained in  the positive  line (or quadrant). We also obtain the asymptotic behaviour of the transition probability density $p(t, x, y) $ when $y\rightarrow 0$. The main tool is the integration by parts formula in stochastic analysis.

报告人简介：胡耀忠，加拿大Alberta大学教授，1992年获法国路易斯巴斯德大学概率博士学位，师从国际著名概率学家P.A.Meyer教授。长期从事随机分析、金融数学的研究，在《Annals of Probability》、《Journal of Theoretical Probability》、《Stochastic Processes and their Applications》、《Probability Theory and Related Fields》以及《SIAM Journal of Control and Optimization》等国际顶尖杂志发表学术论文100余篇。2015年，由于他在随机积分和随机偏微分方程方面的重要工作，当选为Fellow of Institute of Mathematical Statistics。

报告时间：2018年12月27日(星期四)上午9:30-10:30

报告地点：科技楼南楼602